Given quadrilateral ABCD Prove the distance from O to EB B is equal to that from O to ED by Jsxgraph

var board = JXG.JSXGraph.initBoard('box1', {
axis: true, boundingbox: [-15, 15, 15, -15], showcopyright: false,keepaspectratio: true, axis: false, zoom: false,showNavigation: false

var p1 = board.create('point', [-10, 9],{name:'A',fixed:true, size: 1,face:"", color:'blue', label: {offset:[-15,10], color:'blue'}} );
var p2 = board.create('point', [-12, -4],{name:'B',fixed:true, size: 1,face:"", color:'blue', label: {offset:[-15,10], color:'blue'}} );

var p3 = board.create('point', [2, -4],{name:'C', fixed:true,size: 1,face:"", color:'blue', label: {offset:[5,10], color:'blue'}} );
var  a = board.create('slider',[[-4,-12],[4,-12],[-6,-3.20,3.1]], {name:'a'});

var p4 = board.create('point', [function(){return a.Value();}, 9],{name:'D', size: 1,face:"", color:'blue', label: {offset:[5,10], color:'blue'}} );

var l1 = board.create('segment', [p1, p2]);
var l2 = board.create('segment', [p2, p3]);
var l3 = board.create('segment', [p3, p4]);
var l4 = board.create('segment', [p1, p4]);
var l5 = board.create('segment', [p2, p4]);
var bi1 = board.create('bisector', [p2, p3, p4],{visible:false});

var i1 = board.create('intersection', [l1, bi1],{name:'E', face:"",  label: {offset:[-15,0], color:'blue'}} );

var i2 = board.create('intersection', [l5, bi1],{name:'O', face:"",  label: {offset:[0,-15], color:'blue'}} );

var l6 = board.create('segment', [p3, i1]);

var a1 = board.create('nonreflexangle',[p2, p4, p1],{visible: false} );

board.create('text',[-12,14, function(){ return "∠BDA = "+ a1.Value().toFixed(3);}]);

var a2 = board.create('nonreflexangle',[p3, p4, p2],{visible: false} );
var l7 = board.create('segment', [p4, i1]);

board.create('text',[-2,14, function(){ return "∠CDB = "+ a2.Value().toFixed(3);}]);
var pp1 = board.create('perpendicularpoint', [i2, l1],{face:'',label:{offset:[-15,-10]}});
var l8 = board.create('segment', [pp1, i2],{dash:2});
var pp2 = board.create('perpendicularpoint', [i2, l7],{face:'',label:{offset:[-5,15]}});
var l9 = board.create('segment', [pp2, i2],{dash:2});

Triangle posted 1 week ago

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